Sig Fig Checker

the idea

A number carries a promise about how well it was measured.

Every measured value has digits you're sure of plus one last digit you estimated. Those are the significant figures. Zeros are the only tricky part, because some zeros are measured and some are just holding the decimal point in place.

Plant version: if the scale reads 9.00 g, someone saw that last zero on the display, so it counts. If a work order says "1200 lb," you can't tell whether someone weighed it to the pound or rounded to the nearest hundred. That uncertainty is exactly the ambiguity sig figs are trying to capture.

try it

Which digits count?

Type a number (scientific notation works: 6.02e23)

significant captive zero (counts) trailing zero after a decimal (counts) leading zero (never counts) ambiguous trailing zero

Nonzero digits always count. 4.56 has 3.
Captive zeros count (zeros between nonzero digits). 4.05 has 3.
Leading zeros never count. They only place the decimal. 0.0045 has 2.
Trailing zeros count if there's a decimal point. 4.500 has 4. So does 4500. (with a decimal point at the end).
Trailing zeros with no decimal point are ambiguous. 4500 could be 2, 3, or 4. The convention is to count only the nonzero part, so 2. Write it in scientific notation to remove the doubt.
Scientific notation: count only the digits in the front number. 4.50 × 10³ has 3.

the two math rules

Your answer can't be more precise than your worst measurement.

× and ÷

Fewest sig figs wins

Count sig figs in each value. Round the answer to the smallest count.
2.5 × 3.42 = 8.55 → 8.6 (2 sig figs)

+ and −

Fewest decimal places wins

Line up the decimals. Cut the answer at the column of the least precise value.
12.11 + 1.3 = 13.41 → 13.4 (one decimal place)

Why the rules are different: multiplying scales relative error, so what matters is how many digits each value has. Adding stacks absolute error, so what matters is which decimal column each value was measured to. A 1.3 lb reading is only good to the tenths column. Adding it to a 12.11 can't make the tenths column more certain.

Measured value A Operation Measured value B

practice

How many sig figs?

practice

Round it correctly

engineering version

False precision is a data-integrity problem.

A burette read to ±0.05 mL can't support a TA reported to four decimal places, and a spreadsheet that shows 0.873214% isn't more accurate than one that shows 0.87%. It just looks that way. In engineering, the sig figs in a report tell the reader what the instrument could actually resolve. Reporting more digits than that implies a calibration you don't have.

Rule of thumb for lab sheets: carry extra digits through the calculation and round once, at the end. If you round at every step, the rounding errors pile up.

exam traps

Common mistakes

Counting leading zeros in 0.00250. It has 3 sig figs, not 6.
Using the sig-fig rule for addition. Addition uses decimal places.
Rounding in the middle of a multi-step problem. Round only at the end.
Applying sig figs to exact numbers. Counted items (12 eggs) and defined conversions (1 ft = 12 in, 1 kg = 1000 g) have infinite sig figs and never limit your answer.
Writing 1200 when you mean 3 sig figs. Write 1.20 × 10³ or 1200. (with the decimal point).